If `(x+yi)^(3)=u + vi`, prove that `(u)/(x) +(v)/(y) = 4(x^(2)-y^(2))`

If x- yi = (a-bi)/(c-di) , prove that x^(2) + y^(2)= (a^(2) + b^(2))/(c^(2) + d^(2))

If x+ yi= (u+ vi)/(u-yi) , prove that x^(2) + y^(2)=1

If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2)

If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2) .

If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2) .

If y = underset(u(x))overset(v(x))intf(t) dt , let us define (dy)/(dx) in a different manner as (dy)/(dx) = v'(x) f^(2)(v(x)) - u'(x) f^(2)(u(x)) alnd the equation of the tangent at (a,b) as y -b = (dy/dx)_((a,b)) (x-a) If F(x) = underset(1)overset(x)inte^(t^(2)//2)(1-t^(2))dt , then d/(dx) F(x) at x = 1 is

If z= x + yi and |2z + 1| = |z- 2i| , show that 3(x^(2) + y^(2)) + 4(x-y)=3

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))

If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt((1-u^2)/(1-v^2))

If (5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v) : then prove that x : y = u : v .